We are looking for where under the restriction .
Hence, we set , therefore it suffices to find .
Considering the symmetricity, and it suffices to examine the partial derivative of with respect to .
It follows that the critical points are and .
Clearly, .
On the other hand, let
We find that the critical point for is , and , which is the max value of (at ) at the same time because the other critical point makes attain .
Therefore, the given inequality holds.

We are looking for where under the restriction .
Hence, we set , therefore it suffices to find .
Considering the symmetricity, and it suffices to examine the partial derivative of with respect to .
It follows that the critical points are and .
Clearly, .
On the other hand, let
We find that the critical point for is , and , which is the max value of (at ) at the same time because the other critical point makes attain .
Therefore, the given inequality holds.

Not. I know this is a long solution and not so nice. :S

well, the question is supposed to be a Pre-algebra (not calculus) problem. that's what the title of my post says.

well, the question is supposed to be a Pre-algebra (not calculus) problem. that's what the title of my post says.

I know, as I know in JIPAM there are so mant inequalities using convex functions, I guess u wish to see a solution in that direction. But I have no idea since I am not focused on this subject.
I just wanted to share my long and poor solution.